Ways to Assess and Build on Prior Knowledge

Planning Guide: Estimation Strategies

Ways to Assess and Build on Prior Knowledge

Before introducing new material, consider ways to assess and build on students' knowledge and skills related to estimating sums, differences, products and quotients. For example:

· On a trip you travel 4250 km the first week, 3755 km the second week and 2115 km the third week.

i. Estimate how many kilometres you travel during the three weeks. Explain your thinking.

ii. Do you think your estimate is more or less than the calculated answer? Explain your reasoning.

· You have 4 pieces of chocolate that each weigh 253 g. Estimate whether the total weight of these 4 pieces of chocolate is more or less than 1000 g or 1 kg. Explain your thinking.

· During one summer, Marcie travels 7185 km while Jimmy travels 4205 km.

i. Estimate how much farther Marcie travelled than Jimmy during the summer. Explain your thinking.

ii. Do you think your estimate is more or less than the calculated answer? Explain your reasoning.

· You have 62 stickers to share equally among 3 people.

i. Estimate how many stickers each person receives. Explain your thinking.

ii. Do you think your estimate is more or less than the calculated answer? Explain your reasoning.

· Judy used the following estimation strategy to estimate the sum of 365 and 437.

Judy's thinking: I used the front-end strategy. 365 300

437 400

300 + 400 = 700

My estimate for the sum of 365 and 437 is about 700.

How could you adjust Judy's estimate to make it closer to the calculated sum? Explain your thinking without doing the actual calculation.

Subtraction questions: 685 – 217 = ? 685 – 274 = ?

Estimate (front-end strategy): 600 – 200 = 400 600 – 200 = 400

i. Which estimate is closer to the actual difference? Explain your thinking without doing the actual calculation.

ii. For each estimated difference, is 400 an overestimate or an underestimate? Explain your thinking without doing the actual calculation.

If a student appears to have difficulty with these tasks, consider further individual assessment, such as a structured interview, to determine the student's level of skill and understanding. See Sample Structured Interview: Assessing Prior Knowledge and Skills (p. 10).

Sample Structured Interview: Assessing Prior Knowledge and Skills

Directions / Date:
Not Quite There / Ready to Apply
On a trip you travel 4250 km the first week, 3755 km the second week and 2115 km the third week.
a. Estimate how many kilometres you travel during the three weeks. Explain your thinking.
b. Do you think your estimate is more or less than the calculated answer? Explain your reasoning. / Calculates first and then estimates rather than the reverse.
Provides an estimate but is unable to explain his or her thinking.
Does not know whether the estimate is more or less than the calculated answer.
Correctly states that the estimate is more or less than the calculated answer but is unable to explain his or her reasoning. / Uses and explains appropriate estimation strategies, such as the front-end strategy, together with compensation to estimate the sum:
a. Example:
4250 4000
3755 3000
2115 2000
9000
Compensation: 250 + 755 is about 1000. Also, 2115 is 2000 + 115, so I have 115 more to add on.
Final estimate: 9000 + 1000 + 100 = 10 100.
I travel about 10 100 km.
b. 9000 is less than the calculated answer but when I compensated, my final answer of 10 100 is very close to the calculated answer.
You have 4 pieces of chocolate that each weigh 253 g. Estimate whether the total weight of these 4 pieces of chocolate is more or less than 1000 g or 1 kg. Explain your thinking. / Adds 4 and 253 rather than estimating the product of 4 and 253.
Uses an estimation strategy that does not provide an accurate estimate. Provides an accurate estimate but is unable to explain his or her thinking. / Uses a personal estimation strategy to obtain an accurate estimate and explains his or her thinking.
Example: 4 × 253 is a little more than 4 × 250 = 1000.
During one summer, Marcie travels 7185 km while Jimmy travels 4205 km.
a. Estimate how much farther Marcie travelled than Jimmy during the summer. Explain your thinking.
b. Do you think your estimate is more or less than the calculated answer? Explain your reasoning. / Calculates first and then estimates rather than the reverse.
Provides an estimate but is unable to explain his or her thinking.
Does not know whether the estimate is more or less than the calculated answer.
Correctly states that the estimate is more or less than the calculated answer but is unable to explain his or her reasoning. / Uses and explains an appropriate estimation strategy and explains his or her thinking.
Example:
a. 7185 7000
4205 – 4000
Estimate: 3000
The amount dropped off each number is about the same: 185 is about the same as 205. Therefore, the estimate is close to the actual answer.
Marcie travels about 3000 km farther than Jimmy during the summer.
b. Since 205 is slightly more than 185, then the estimate is slightly more than the calculated answer.
You have 62 stickers to share equally among 3 people.
a. Estimate how many stickers each person receives. Explain your thinking.
b. Do you think your estimate is more or less than the calculated answer? Explain your reasoning. / Does not know which operation to use in the estimated answer.
Calculates first and then estimates rather than the reverse.
Provides an estimate but is unable to explain his or her thinking.
Does not know whether the estimate is more or less than the calculated answer.
Correctly states that the estimate is more or less than the calculated answer but is unable to explain his or her reasoning. / Uses and explains an appropriate estimation strategy and explains his or her thinking.
Example:
a. 62 3 is close to
60 3 = 20.
Each person receives about 20 stickers.
b. The estimate is less than the calculated answer because 60 is less than 62.
Judy used the following estimation strategy to estimate the sum of 365 and 437.
Judy's thinking: "I used the front-end strategy:
365 300
437 400
300 + 400 = 700
My estimate for the sum of 365 and 437 is about 700."
How could you adjust Judy's estimate to make it closer to the calculated sum? Explain your thinking without doing the actual calculation. / Does not know how to adjust Judy's estimate to make it closer.
Provides a closer estimate; e.g., 800, but does not explain his or her reasoning. / Uses compensation to adjust Judy's estimate and explains the process.
Example:
65 was dropped off 365 to make 300. 37 was dropped off 437 to make 400.
65 + 37 is about 100.
A better estimate is
700 + 100 = 800.
Present the following two subtraction questions and their estimated differences to the student:
Subtraction questions:
1. 685 – 217 = ?
2. 685 – 274 = ?
Estimate (front-end strategy):
1. 685 – 217 = ?
600 – 200 = 400
2. 685 – 274 = ?
600 – 200 = 400
Ask the students:
a. Which estimate is closer to the actual difference? Explain your thinking without doing the actual calculation.
b. For each estimated difference, is 400 an overestimate or an underestimate? Explain your thinking without doing the actual calculation. / Does not know which estimate is closer to the actual difference.
States which estimate is closer to the actual difference but does not explain his or her thinking.
Does not know whether the 400 is an overestimate or an underestimate.
States that 400 is an overestimate in at least one of the examples but does not explain why. / a. States that the estimated answer of 400 is a closer estimate for question 1 than for question 2. For question2, about the same amount is dropped off each number in the front-end strategy; therefore, the estimate is close. For question 1, 85 is dropped off the first number and only 17 is dropped of the second number so the estimate will not be as close.
b. In each case, 400 is an underestimate because you must consider the difference of 85 – 17 and also 85 – 74. The difference in each case must be added on to the 400 to make a closer estimate.